The first task consists in mitigating inequalities of exposure between (groups of) items, and appears in many studies [1]}, [2]}, [3]}. This leads to a trade-off between the total utility of users and inequality among items, and such inequalities are usually measured by the Gini index (as in [4]}, [5]}). Removing the dependency on \(P\)  to lighten the notation, a natural formulation of this trade-off uses the two-sided GGF (REF ) by setting \({w^1}= (1,\ldots ,1)\)  and \({w^2}= \left(\frac{m-j+1}{m}\right)_{j=1}^m\) , which yields:
\(\displaystyle g^{\rm user}({u})=\frac{1}{n}\sum _{i=1}^n{u}_i\quad \quad g^{\rm item}({v})=\sum _{j=1}^m \frac{m-j+1}{m} {v}_j^\uparrow .\) 
